and \(_{1}, \dots , _{t}\)  are independent draws from a distribution \(^{\prime }\)  which is \(2^{-p}\) -close to \(\) . For estimating \(Z\) , we use an \(\ell _p\) -sketch to accuracy \(/2\)  and failure probability \(\delta = o(1)\) . For example, the sketch for \(Z\)  may proceed by applying an \(\ell _p\) -sketch [1]} to the stacked vector \(x^{\prime } \in ^{nd}\)  where
\(x_{ij}^{\prime } = \lambda _i^{1/p} \cdot x_{ij},\) 
